A Preconditioned Fast Finite Volume Method for Distributed-Order Diffusion Equation and Applications
Year: 2019
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 1 : pp. 28–44
Abstract
A Crank-Nicolson finite volume scheme for the modeling of the Riesz space distributed-order diffusion equation is proposed. The corresponding linear system has a symmetric positive definite Toeplitz matrix. It can be efficiently stored in $\mathcal{O}$($NK$) memory. Moreover, for the finite volume scheme, a fast version of conjugate gradient (FCG) method is developed. Compared with the Gaussian elimination method, the computational complexity is reduced from $\mathcal{O}$($MN$3 + $NK$) to $\mathcal{O}$($l$$A$$MN$log$N$ + $NK$), where $l$$A$ is the average number of iterations at a time level. Further reduction of the computational cost is achieved due to use of a circulant preconditioner. The preconditioned fast finite volume method is combined with the Levenberg-Marquardt method to identify the free parameters of a distribution function. Numerical experiments show the efficiency of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.160418.190518
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 1 : pp. 28–44
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Distributed-order diffusion equation finite volume method fast conjugate gradient method circulant preconditioner parameter identification.
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